Cycles in projective spaces

Aceves, Elaina; Heywood, David; Klahr, Ashley; Vega, Oscar

doi:10.1007/s00022-013-0198-7

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [21] Lazebnik, Mellinger, and Vega demonstrate that it is possible to embed a 2k-cycle of every possible size into the Levi graph of any finite affine or projective plane. This was further extended by Aceves, Heywood, Klahr, and Vega [1] who showed that one can embed a 2k-cycle of every possible size into the Levi graph of the projective space P G(d, q). Moreover, in a different paper Lazebnik, Mellinger, and Vega [22] motivated the study of counting 2k-cycles in the Levi graph with the following two questions.…”

Section: Introductionmentioning

confidence: 87%

On the number of $k$-gons in finite projective planes

Taranchuk

2021

Preprint

View full text Add to dashboard Cite

Let Π be a projective plane of order n and Γ Π be its Levi graph (the point-line incidence graph). For fixed k ≥ 3, let c 2k (Γ Π ) denote the number of 2k-cycles in Γ Π . In this paper we show thatWe also state a conjecture regarding the third and fourth largest terms in the asymptotic of the number of 2k-cycles in Γ Π . Let ex(v, C 2k , C odd ∪ {C 4 }) denote the greatest number of 2k-cycles amongst all bipartite graphs of order v and girth at least 6. As a corollary of the result above, we obtain

show abstract

Section: Introductionmentioning

confidence: 87%